I am reading Ortin's Gravity and Strings and trying to understand the generalisation of Newtonian Gravity to a relativistic field theory. On page 47 (link above) he motivates the study of the Poisson ...

I am trying to prove the Lorentz invariance of the (left-handed) Weyl Lagrangian:
$$\mathcal L=i\psi^\dagger\bar\sigma^\mu\partial_\mu\psi$$
A Lorentz transformation is realized as
$\psi\to M\psi$, ...

I have a question regarding Noether's theorem. In our introductory QFT class (which is based on the book by Michele Maggiore) we have derived the Noether currents in the same form as displayed in this ...

To avoid ambiguity, this question pertains to the construction of Lagrangian densities (including interaction terms) in terms of their values at single points in spacetime.
In classical mechanics in ...

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space?
As I guess, I thought one way would be to generalize 3-force to 4-force and replace the 3-gradient with the ...

In supermultiplets, the bosonic degrees of freedom and the fermionic degrees of freedom need to match in number. The number of degrees of freedom of a field corresponds to the number of independent ...

How can I find the mass spectrum of a field theory given a Lagrangian made of a canonical kinetic term and a potential. I mean, I think I have to find the matrix of the quadratical terms in all the ...

I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit ...

I am learning classical field theory and am trying to find the momentum density of the electromagnetic lagrangian as part of an example of Noether's Theorem. The derivative I am encountering is:
$$
...

If I have a number of particles interacting with one another locally, then the center of mass of the system moves along a geodesic. Taking this further with the particles interacting via an EM field, ...

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean):
$$
\mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu}
$$
...

In the introduction of chapter-12 of “An Introduction to Quantum Field Theory” by Peskin and Schroeder I encountered this line: “The quantum fluctuatuations at arbitrarily short distances appear in ...

This may be a very blunt question but I wonder why we always use Poincare invariant Lagrangians in field theory. After all, the entire world around us is by no means homogeneous, isotropic and so on. ...

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...

We know that,the shape of electric field line in a cylinder under varying magnetic field is circle,and I wonder,what's the situation if it is a piece of metal with rectangular cross section?
I think ...

Suppose I have an Lagrangian $$\mathcal{L} = \frac{1}{2}g_{ab} \bar{\psi}^a \Gamma^k \partial_k \psi^b $$ and I want to show it's invariance under the infinitesimal Lorentz transformations $$\delta ...

My question is about the derivation of Ward identities. I will sketch it here in the case of an O(N) symmetric model and point out what it bothering me when I am done. I am being very sloppy with the ...

In free field theory, the full list of conformal primaries, is given by the Twist-2 operators. These have $\Delta = l+2$, which is also the saturation condition for the unitarity bound for $l \neq 0$. ...

Following my earlier question in this Phys.SE post I have another question regarding the derivation I am struggling through!
Considering the variation in the Lagrange density for $x'=x+\delta x$ and ...

I'm finding the field equations for a hypothetical Lagrangian with dependence on the second derivative of a scalar field, $L\left(\phi,\phi_{,\mu},\phi_{,\mu\nu}\right)$, and in the analogue to the ...

I am trying to understand the continuum version of Noethers theorem from this source (p 15- 17) however I am stuck on a couple of points. I will go through what I have so far and then ask my questions ...

In integrable systems, for example in the XXX spin chain, one encounters non-local charges (that form a Yangian). They are fine since the Yangian generate an infinite number of them, which gives us ...